Which of the following numbers is a factor of 196? ${3,4,8,10,12}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $196$ by each of our answer choices. $196 \div 3 = 65\text{ R }1$ $196 \div 4 = 49$ $196 \div 8 = 24\text{ R }4$ $196 \div 10 = 19\text{ R }6$ $196 \div 12 = 16\text{ R }4$ The only answer choice that divides into $196$ with no remainder is $4$ $ 49$ $4$ $196$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $4$ are contained within the prime factors of $196$ $196 = 2\times2\times7\times7 4 = 2\times2$ Therefore the only factor of $196$ out of our choices is $4$. We can say that $196$ is divisible by $4$.